In youngs experiment a mixture of orange light 611 nm and bl

In young\'s experiment a mixture of orange light (611 nm) and blue light(471 nm) shines on the double slit. The centers of the first order bright blue lie at the outer edges of a screen that is located 0.540 m away from the slits. However, the first-order bright orange fringes fall of the screen. By how much and in which direction(toward or away from the slits) should the screen be moved, as that the centers of the first-order bright orange fringes will just appear on the screen? It may be assumed that theta is small, so that sin theta = tan theta. distance m direction

Solution

d sin theta = m lambda and y = L tan theta

y / L = m lambda / d

With m = 1, L = y d / lambda, y an d are same

L_blue / L_orange = lambda_orange / lambda_blue

L_blue - L_orange = L_blue - (lambda_orange * L_blue / lambda_blue)

= L_blue * (1 - lambda_orange / lambda_blue)

= 0.540 * (1 - 471/611)

= 0.124 m